78 citations · 1.2k across the 112 of their papers we have counts for
98 papers · 1 filter
Sophus Lie's problem on two-dimensional metrics with projective symmetries: completing the local classification
Gianni Manno, Vladimir S. Matveev, Filippo Salis
We complete the local classification, up to isometry, of -dimensional pseudo-Riemannian metrics (i.e. both Riemannian and Lorentzian), admitting a projective symmetry algebra of…
Quadratic Killing tensors on classical Lie groups are decomposable
Vladimir Matveev, An Ky Nguyen, Yuri Nikolayevsky
A Killing tensor field on a Riemannian manifold is a covariant symmetric tensor field whose contraction with the velocity vector along a geodesic produces a homogeneous pol…
Local description of gl-regular Haantjes operators
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We study Haantjes operators, that is, (1,1)-tensor fields with vanishing Haantjes torsion. Our main result is a complete local description of gl-regular Haantjes operators. Additio…
On Killing tensors on Riemannian symmetric spaces
Vladimir Matveev, Yuri Nikolayevsky
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynom…
Duality of operator Frobenius algebras and solution of Eisenhart-Stäckel problem in the non-diagonal case
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We study Frobenius algebras of operator fields and introduce a novel notion of duality for them. We show that, under the assumption that the operator fields forming the Frobenius a…
Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere whose magnetic 2-form is…
On Separation of Variables for Symmetric Spaces of Rank1
Alexey Bolsinov, Holger R. Dullin, Vladimir. S. Matveev +1
We study existence and nonexistence of diagonal and separating coordinates for Riemannian symmetric spaces of rank 1. We generalize the results of Gauduchon and Moroianu, 2020, by…
On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We explore the Jordan-Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field $L…
Self-adjoint quantization of Stäckel integrable systems
Jonathan M Kress, Vladimir Matveev
We show that quadratic Hamiltonians in involution coming from a Stäckel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols…
Variationality of conformal geodesics in dimension 3
Boris Kruglikov, Vladimir S. Matveev, Wijnand Steneker
Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The e…
Research problems on relations between Nijenhuis geometry and integrable systems
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geome…
On the existence of geodesic vector fields on closed surfaces
Vladimir S. Matveev
We construct an example of a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
Sergey I. Agafonov, Vladimir S. Matveev
We show that if functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an -dimensional mani…
Killing tensors on reducible spaces
Vladimir S. Matveev, Yuri Nikolayevsky
We prove that on the product of two Riemannian manifolds one of which is compact, any Killing tensor is reducible, that is, is the sum of products of Killing tensors on the factors…
Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields
Vladimir S. Matveev, Yuri Nikolayevsky
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fiel…
When a -tensor generates separation of variables of a certain metric
Andrey Yu. Konyaev, Jonathan M. Kress, Vladimir S. Matveev
By a -tensor field , we construct an explicit system of differential invariants that vanish if and only if there (locally) exists a metric for which generates…
Applications of Nijenhuis Geometry V: geodesically equivalent metrics and finite-dimensional reductions of certain integrable quasilinear systems
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We describe all metrics geodesically compatible with a gl-regular Nijenhuis operator . The set of such metrics is large enough so that a generic local curve is a geodesic fo…
Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl-regular Nijenhuis operators. We prove the splitting Theorem for symmetri…
Canonical curves and Kropina metrics in Lagrangian contact geometry
T. Ma, K. J. Flood, V. S. Matveev +1
We present a Fefferman-type construction from Lagrangian contact to conformal structures and examine several related topics. In particular, we concentrate on describing the canonic…
Orthogonal separation of variables for spaces of constant curvature
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating…
Almost every path structure is not variational
Boris S. Kruglikov, Vladimir S. Matveev
Given a smooth family of unparameterized curves such that through every point in every direction there passes exactly one curve, does there exist a Lagrangian with extremals being…
Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We consider multicomponent local Poisson structures of the form , under the assumption that the third order term is Darboux-Poisson and…
Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
S. Bandyopadhyay, B. Dacorogna, V. S. Matveev +1
We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give exp…
Geodesic random walks, diffusion processes and Brownian motion on Finsler manifolds
Tianyu Ma, Vladimir S. Matveev, Ilya Pavlyukevich
We show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to…